∃x ∈ ]a, b[ , φ
where
φ
is not conjunction
Let's simplify it.
For instance, ∃x
∈ ]a, b[, (P > 0) or (Q < 0) can rewritten
in ∃x
∈ ]a, b[, (P > 0) or ∃x ∈ ]a, b[, (Q < 0).
If
φ is more complicated, consider a disjonctive normal form of
φ. Then distribute the or
operators over the ∃ quantifier. You obtain a disjonction of formulas
of the form ∃x
∈ ]a, b[, ψ
where ψ is a
conjunction.
Click here to eliminate
the
quantifier ∃ in each of these
∃x ∈ ]a,
b[, ψ!